Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

A lower bound for the permanent of a $ (0,\,1)$-matrix


Author: P. M. Gibson
Journal: Proc. Amer. Math. Soc. 33 (1972), 245-246
MSC: Primary 15A15
DOI: https://doi.org/10.1090/S0002-9939-1972-0294360-5
MathSciNet review: 0294360
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let $ A = ({a_{ij}})$ be an n-square fully indecomposable $ (0,1)$-matrix. It is shown that if each row sum of A is at least k then per $ A \geqq \sum \nolimits_{i,j = 1}^n{a_{ij}} - 2n + 2 + \sum \nolimits_{m = 1}^{k - 1}(m! - 1)$. This improves an inequality obtained by H. Minc.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 15A15

Retrieve articles in all journals with MSC: 15A15


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1972-0294360-5
Keywords: Bounds for the permanent, fully indecomposable matrices, nearly decomposable matrices, $ (0,1)$-matrices
Article copyright: © Copyright 1972 American Mathematical Society